Thomas was a son of John (or Roger) & Mary Burlingame. His brother John Jr. married Mary Lippitt, his wife's sister.
The will of Thomas Burllingame of Cranston, yeoman, dated 6 June 1756 (proved 1758) mentions wife Hannah; sons: Thomas, Moses, Peter, Joshua, and Stephen; dtrs: Margaret Remington, Sarah Briggs, Freelove Gorton, Alice Westcot, and Patience Burllingame; grandsons Samuel Burllingame and John Warner; granddaughter Freelove Arnold.
I have roughly estimated the birth years of some of Thomas's children.